Understanding Altitudes and Slopes

The video tutorial explains how to find the equation of an altitude in a triangle. It begins by identifying the properties of altitudes and the need for a point and a slope to determine an equation. The instructor calculates the slope of line BC and uses the concept of opposite reciprocals to find the slope of the altitude. Finally, the equation of the altitude is derived using the known point and slope.

What is the primary characteristic of an altitude in a triangle?

• It is perpendicular to the opposite side.

• It divides the triangle into two equal areas.

• It is parallel to the base.

• It bisects the angle at the vertex.

What information is essential to find the equation of a line?

• Two points on the line.

• The color of the line.

• The length of the line.

• The area of the triangle.

If you know the slope of one line, how can you find the slope of a perpendicular line?

• Take the negative reciprocal.

• Square the slope.

• Double the slope.

• Add 1 to the slope.

What is the slope of line BC if the rise is 8 and the run is -2?

• -4

• 4

• 2

• -2

How do you find the slope of an altitude if you know the slope of the base?

• Use the same slope.

• Subtract 1 from the base's slope.

• Use the opposite reciprocal of the base's slope.

• Add 1 to the base's slope.

What is the y-intercept of the altitude if it passes through the point (0, 2)?

• 3

• 0

• 1

• 2

What is the equation of the altitude if its slope is 1/4 and it passes through (0, 2)?

• y = 4x + 1/2

• y = 1/4x + 2

• y = 2x + 1/4

• y = 1/2x + 4